Question

Find two positive numbers x and y, such that x + y = 60 and xy is maximum.
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Answer 1

Answer:

The two positive numbers are 30, 30.

Step-by-step explanation:

Let P = xy

Given, x+y = 60

x = 60 - y

P = (60 - y) y

P = 60y - y²

dP/dy = 60 - 2y

dP/ dy = 0

60 - 2y = 0

y = 30

Now,

d²P/dy = -2y

putting y = 30

= -2(30)

-60 <0

So, at y = 30 xy is maximum.

Therefore, if u = 30

then

x+y = 60

x = 30

So the two positive numbers are 30, 30.

Answer 2

Answer:

please comment me my answer

Step-by-step explanation:

Let P=xy

3

It is given that x+y=60

⇒x=60−y

P=(60−y)y

3

[Putting value of x]

=60y

3

−y

4

⇒

dy

dP

=180y

2

−4y

3

dy

2

d

2

P

=360y−12y

2

For maximum or minimum values of y, P we have

dy

dP

=0

⇒180y

2

−4y

3

=0

⇒4y

2

(45−y)=0

⇒y=0 45−y=0 y=45

Now (

dy

2

d

2

P

)

y=45

=360×45−12(45)

2

=12×45−(30−45)

=−8100<0

P is maximum when y=45

when y=45 x+y=60 ⇒x=60−45

x=15

Numbers are 15 and 45